Abstract : I will present an analytical description of radiative emission from sub-wavelength emitters embedded in triply resonant nonlinear χ(2) cavities supporting exceptional points (EP) comprised of dark and leaky modes. I will show that the up-converted radiation rate of an emitter in such a system can be greatly enhanced—by two orders of magnitude—compared to typical Purcell factors achievable in non-degenerate cavities, for both monochromatic and broadband emitters. We provide a proof-of-concept implementation of such a scheme that employs topology optimization techniques to realize a 2D photonic-crystal slab supporting an EP formed out of a Dirac cone at the emission frequency and a phase-matched, leaky-mode resonance at the second harmonic frequency.